{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 逻辑回归预测考试通过"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**任务:**\n",
    "\n",
    "基于examdata.csv数据，建立逻辑回归模型\n",
    "预测Exam1 = 75, Exam2 = 60时，该同学在Exam3是 passed or failed;\n",
    "建立二阶边界，提高模型准确度"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "@Author  : Flare Zhao\n",
    "@QQ-Email & Wechat: 454209979\n",
    "@QQ讨论群：530533630  申请加群的验证信息为订单号（粘贴号码数字即可）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Exam1</th>\n",
       "      <th>Exam2</th>\n",
       "      <th>Pass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Exam1      Exam2  Pass\n",
       "0  34.623660  78.024693     0\n",
       "1  30.286711  43.894998     0\n",
       "2  35.847409  72.902198     0\n",
       "3  60.182599  86.308552     1\n",
       "4  79.032736  75.344376     1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#load the data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "data = pd.read_csv('examdata.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualize the data\n",
    "%matplotlib inlineIN\\COOCARE.EXE\" \\MOUSE\n",
    "\n",
    "\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "fig1 = plt.figure()\n",
    "plt.scatter(data.loc[:,'Exam1'],data.loc[:,'Exam2'])\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     False\n",
      "1     False\n",
      "2     False\n",
      "3      True\n",
      "4      True\n",
      "      ...  \n",
      "95     True\n",
      "96     True\n",
      "97     True\n",
      "98     True\n",
      "99     True\n",
      "Name: Pass, Length: 100, dtype: bool\n"
     ]
    }
   ],
   "source": [
    "#add label mask\n",
    "mask=data.loc[:,'Pass']==1\n",
    "print(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2 = plt.figure()\n",
    "passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])\n",
    "failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    34.623660\n",
       "1    30.286711\n",
       "2    35.847409\n",
       "3    60.182599\n",
       "4    79.032736\n",
       "Name: Exam1, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#dafine X,y\n",
    "X = data.drop(['Pass'],axis=1)\n",
    "y = data.loc[:,'Pass']\n",
    "X1 = data.loc[:,'Exam1']\n",
    "X2 = data.loc[:,'Exam2']\n",
    "X1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2) (100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape,y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  display: none;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  overflow: visible;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".estimator-table summary {\n",
       "    padding: .5rem;\n",
       "    font-family: monospace;\n",
       "    cursor: pointer;\n",
       "}\n",
       "\n",
       ".estimator-table details[open] {\n",
       "    padding-left: 0.1rem;\n",
       "    padding-right: 0.1rem;\n",
       "    padding-bottom: 0.3rem;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table {\n",
       "    margin-left: auto !important;\n",
       "    margin-right: auto !important;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:nth-child(odd) {\n",
       "    background-color: #fff;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:nth-child(even) {\n",
       "    background-color: #f6f6f6;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:hover {\n",
       "    background-color: #e0e0e0;\n",
       "}\n",
       "\n",
       ".estimator-table table td {\n",
       "    border: 1px solid rgba(106, 105, 104, 0.232);\n",
       "}\n",
       "\n",
       ".user-set td {\n",
       "    color:rgb(255, 94, 0);\n",
       "    text-align: left;\n",
       "}\n",
       "\n",
       ".user-set td.value pre {\n",
       "    color:rgb(255, 94, 0) !important;\n",
       "    background-color: transparent !important;\n",
       "}\n",
       "\n",
       ".default td {\n",
       "    color: black;\n",
       "    text-align: left;\n",
       "}\n",
       "\n",
       ".user-set td i,\n",
       ".default td i {\n",
       "    color: black;\n",
       "}\n",
       "\n",
       ".copy-paste-icon {\n",
       "    background-image: url();\n",
       "    background-repeat: no-repeat;\n",
       "    background-size: 14px 14px;\n",
       "    background-position: 0;\n",
       "    display: inline-block;\n",
       "    width: 14px;\n",
       "    height: 14px;\n",
       "    cursor: pointer;\n",
       "}\n",
       "</style><body><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LogisticRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.7/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
       "        <div class=\"estimator-table\">\n",
       "            <details>\n",
       "                <summary>Parameters</summary>\n",
       "                <table class=\"parameters-table\">\n",
       "                  <tbody>\n",
       "                    \n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('penalty',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">penalty&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;l2&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('dual',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">dual&nbsp;</td>\n",
       "            <td class=\"value\">False</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('tol',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">tol&nbsp;</td>\n",
       "            <td class=\"value\">0.0001</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('C',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">C&nbsp;</td>\n",
       "            <td class=\"value\">1.0</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('fit_intercept',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">fit_intercept&nbsp;</td>\n",
       "            <td class=\"value\">True</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('intercept_scaling',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">intercept_scaling&nbsp;</td>\n",
       "            <td class=\"value\">1</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('class_weight',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">class_weight&nbsp;</td>\n",
       "            <td class=\"value\">None</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('random_state',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">random_state&nbsp;</td>\n",
       "            <td class=\"value\">None</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('solver',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">solver&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;lbfgs&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('max_iter',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">max_iter&nbsp;</td>\n",
       "            <td class=\"value\">100</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('multi_class',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">multi_class&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;deprecated&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('verbose',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">verbose&nbsp;</td>\n",
       "            <td class=\"value\">0</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('warm_start',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">warm_start&nbsp;</td>\n",
       "            <td class=\"value\">False</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('n_jobs',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">n_jobs&nbsp;</td>\n",
       "            <td class=\"value\">None</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('l1_ratio',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">l1_ratio&nbsp;</td>\n",
       "            <td class=\"value\">None</td>\n",
       "        </tr>\n",
       "    \n",
       "                  </tbody>\n",
       "                </table>\n",
       "            </details>\n",
       "        </div>\n",
       "    </div></div></div></div></div><script>function copyToClipboard(text, element) {\n",
       "    // Get the parameter prefix from the closest toggleable content\n",
       "    const toggleableContent = element.closest('.sk-toggleable__content');\n",
       "    const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';\n",
       "    const fullParamName = paramPrefix ? `${paramPrefix}${text}` : text;\n",
       "\n",
       "    const originalStyle = element.style;\n",
       "    const computedStyle = window.getComputedStyle(element);\n",
       "    const originalWidth = computedStyle.width;\n",
       "    const originalHTML = element.innerHTML.replace('Copied!', '');\n",
       "\n",
       "    navigator.clipboard.writeText(fullParamName)\n",
       "        .then(() => {\n",
       "            element.style.width = originalWidth;\n",
       "            element.style.color = 'green';\n",
       "            element.innerHTML = \"Copied!\";\n",
       "\n",
       "            setTimeout(() => {\n",
       "                element.innerHTML = originalHTML;\n",
       "                element.style = originalStyle;\n",
       "            }, 2000);\n",
       "        })\n",
       "        .catch(err => {\n",
       "            console.error('Failed to copy:', err);\n",
       "            element.style.color = 'red';\n",
       "            element.innerHTML = \"Failed!\";\n",
       "            setTimeout(() => {\n",
       "                element.innerHTML = originalHTML;\n",
       "                element.style = originalStyle;\n",
       "            }, 2000);\n",
       "        });\n",
       "    return false;\n",
       "}\n",
       "\n",
       "document.querySelectorAll('.fa-regular.fa-copy').forEach(function(element) {\n",
       "    const toggleableContent = element.closest('.sk-toggleable__content');\n",
       "    const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';\n",
       "    const paramName = element.parentElement.nextElementSibling.textContent.trim();\n",
       "    const fullParamName = paramPrefix ? `${paramPrefix}${paramName}` : paramName;\n",
       "\n",
       "    element.setAttribute('title', fullParamName);\n",
       "});\n",
       "</script></body>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#establish the model and train it\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "LR = LogisticRegression()\n",
    "LR.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1\n",
      " 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1\n",
      " 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "#show the predicted result and its accuracy\n",
    "y_predict = LR.predict(X)\n",
    "print(y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.89\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy =  accuracy_score(y,y_predict)\n",
    "print(accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "passed\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Dev\\anaconda3\\envs\\sklearn\\Lib\\site-packages\\sklearn\\utils\\validation.py:2749: UserWarning: X does not have valid feature names, but LogisticRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "#exam1=70,exam2=65\n",
    "y_test = LR.predict([[70,65]])\n",
    "print('passed' if y_test==1 else 'failed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.20535491, 0.2005838 ]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LR.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-25.05219314])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LR.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-25.05219314] 0.2053549121779038 0.20058380395469044\n"
     ]
    }
   ],
   "source": [
    "theta0 = LR.intercept_\n",
    "theta1,theta2 = LR.coef_[0][0],LR.coef_[0][1]\n",
    "print(theta0,theta1,theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     89.449169\n",
      "1     93.889277\n",
      "2     88.196312\n",
      "3     63.282281\n",
      "4     43.983773\n",
      "        ...    \n",
      "95    39.421346\n",
      "96    81.629448\n",
      "97    23.219064\n",
      "98    68.240049\n",
      "99    48.341870\n",
      "Name: Exam1, Length: 100, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "X2_new = -(theta0+theta1*X1)/theta2\n",
    "print(X2_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig3 = plt.figure()\n",
    "passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])\n",
    "failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])\n",
    "plt.plot(X1,X2_new) # 边界曲线\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "边界函数： $\\theta_0 + \\theta_1 X_1 + \\theta_2 X_2 = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![linear_boundary.png](images/linear_boundary.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "边界函数： $\\theta_0 + \\theta_1 X_1 + \\theta_2 X_2 = 0$\n",
    "\n",
    "二阶边界函数：$\\theta_0 + \\theta_1 X_1 + \\theta_2 X_2+ \\theta_3 X_1^2 + \\theta_4 X_2^2 + \\theta_5 X_1 X_2 = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create new data\n",
    "X1_2 = X1*X1\n",
    "X2_2 = X2*X2\n",
    "X1_X2 = X1*X2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           X1         X2         X1_2         X2_2        X1_X2\n",
      "0   34.623660  78.024693  1198.797805  6087.852690  2701.500406\n",
      "1   30.286711  43.894998   917.284849  1926.770807  1329.435094\n",
      "2   35.847409  72.902198  1285.036716  5314.730478  2613.354893\n",
      "3   60.182599  86.308552  3621.945269  7449.166166  5194.273015\n",
      "4   79.032736  75.344376  6246.173368  5676.775061  5954.672216\n",
      "..        ...        ...          ...          ...          ...\n",
      "95  83.489163  48.380286  6970.440295  2340.652054  4039.229555\n",
      "96  42.261701  87.103851  1786.051355  7587.080849  3681.156888\n",
      "97  99.315009  68.775409  9863.470975  4730.056948  6830.430397\n",
      "98  55.340018  64.931938  3062.517544  4216.156574  3593.334590\n",
      "99  74.775893  89.529813  5591.434174  8015.587398  6694.671710\n",
      "\n",
      "[100 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "X_new = {'X1':X1,'X2':X2,'X1_2':X1_2,'X2_2':X2_2,'X1_X2':X1_X2}\n",
    "X_new = pd.DataFrame(X_new)\n",
    "print(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#establish new model and train\n",
    "LR2 = LogisticRegression()\n",
    "LR2.fit(X_new,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "y2_predict = LR2.predict(X_new)\n",
    "accuracy2 = accuracy_score(y,y2_predict)\n",
    "print(accuracy2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     34.623660\n",
      "1     30.286711\n",
      "2     35.847409\n",
      "3     60.182599\n",
      "4     79.032736\n",
      "        ...    \n",
      "95    83.489163\n",
      "96    42.261701\n",
      "97    99.315009\n",
      "98    55.340018\n",
      "99    74.775893\n",
      "Name: Exam1, Length: 100, dtype: float64 63    30.058822\n",
      "1     30.286711\n",
      "57    32.577200\n",
      "70    32.722833\n",
      "36    33.915500\n",
      "        ...    \n",
      "56    97.645634\n",
      "47    97.771599\n",
      "51    99.272527\n",
      "97    99.315009\n",
      "75    99.827858\n",
      "Name: Exam1, Length: 100, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "X1_new = X1.sort_values()\n",
    "print(X1,X1_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "边界函数： $\\theta_0 + \\theta_1 X_1 + \\theta_2 X_2 = 0$\n",
    "\n",
    "二阶边界函数：$\\theta_0 + \\theta_1 X_1 + \\theta_2 X_2+ \\theta_3 X_1^2 + \\theta_4 X_2^2 + \\theta_5 X_1 X_2 = 0$\n",
    "\n",
    "$a x^2 + b x + c=0: x1 = (-b+(b^2-4ac)^.5)/2a,x1 = (-b-(b^2-4ac)^.5)/2a$\n",
    "\n",
    "$\\theta_4 X_2^2 + (\\theta_5 X_1++ \\theta_2) X_2 + (\\theta_0 + \\theta_1 X_1 + \\theta_3 X_1^2)=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63    132.124249\n",
      "1     130.914667\n",
      "57    119.415258\n",
      "70    118.725082\n",
      "36    113.258684\n",
      "         ...    \n",
      "56     39.275712\n",
      "47     39.251001\n",
      "51     38.963585\n",
      "97     38.955634\n",
      "75     38.860426\n",
      "Name: Exam1, Length: 100, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "theta0 = LR2.intercept_\n",
    "theta1,theta2,theta3,theta4,theta5 = LR2.coef_[0][0],LR2.coef_[0][1],LR2.coef_[0][2],LR2.coef_[0][3],LR2.coef_[0][4]\n",
    "a = theta4\n",
    "b = theta5*X1_new+theta2\n",
    "c = theta0+theta1*X1_new+theta3*X1_new*X1_new\n",
    "X2_new_boundary = (-b+np.sqrt(b*b-4*a*c))/(2*a)\n",
    "\n",
    "print(X2_new_boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig5 = plt.figure()\n",
    "passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])\n",
    "failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])\n",
    "plt.plot(X1_new,X2_new_boundary)\n",
    "plt.title('Exam1-Exam2')\n",
    "plt.xlabel('Exam1')\n",
    "plt.ylabel('Exam2')\n",
    "plt.legend((passed,failed),('passed','failed'))\n",
    "plt.show()\n",
    "\n",
    "plt.plot(X1_new,X2_new_boundary)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
